Bachelor project presentation: Vlad Malai
|When:||Fr 21-01-2022 10:00 - 10:30|
Local and Global Symmetries of PDE's
We look into the theoretical framework developed by Sophus Lie in his study of differential equations, and determine correspondingly, using the developed techniques, the known Lie point symmetries of several PDEs: logistic equation, Schrödinger equation, Burgers' equation. Subsequently we look whether the local symmetry group can be extended to a global one. The analysis of the Schrödinger equation shows that its symmetries form a global group under Craddock's theorem and in the case of Burgers' equation one can use a 1-1 mapping to the solutions of the heat equation to establish a globalization theorem. We end by mentioning an example from the literature, a specific filtration equation, for which non- globalizable symmetries have been found.
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Meeting ID: 864 3778 4476